3B Scientific Critical Point Apparatus - Manual (Page 19)

5
ϑ ⋅ − ⋅ + + =
ϑ
C p C s s s
p e 0
(9)
By substituting in equation 4, we get:
( )
0
0
0 = ⋅ −
ϑ + ϑ
⋅ ϑ ⋅ β − ⋅ β + + ⋅
ϑ
R n
A p s s p
p e
(10)
If we take several readings at various temperatures
and pressures, we can calculate the term:
( )
∑
=
ϑ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⋅ −
ϑ + ϑ
⋅ ϑ ⋅ β − ⋅ β + + ⋅
=
n
p
R n
A p s s p
Q
1 i
2
0
i i 0 i i
(11)
The free parameters s
0
,
β
P
,
β
ϑ
and n should be appro-
priately selected so that the value of Q is reduced to a
minimum.
Additionally required (see also chapter 8):
1 Compressor or
bicycle pump and valve
1 Bath/circulating thermostat U14400
1 Dig. quick-response pocket thermometer U11853
1 Type K NiCr-Ni immersion sensor,
-65°C-550°C U11854
2 Silicone tubes, 1 m U10146
1 l Anti-freeze fluid with corrosion-inhibiting additive
for aluminium engines (e.g., Glysantin® G30 ma-
nufactured by BASF)
Conducting the calibration:
• Connect the circulation thermostat as described
in chapter 8 and fill it with the water/anti-freeze
mixture.
• Connect the plastic tube (3-mm internal diameter)
to the 1/8" gas connection fittings.
• Open the regulating valve.
• Wind the handwheel outwards, making the piston
move till it reaches say the 46.0 mm position.
• Use a compressor or a bicycle pump to create an
excess air pressure of approx. 3-8 bar in the
measuring cell.
• Shut the regulating valve.
• To record measurements, vary the volume in the
measuring cell or the temperature of the thermo-
stat and wait till a stationary equilibrium has
been attained. Then take a pressure reading.
• Use appropriate adjustment software to set the s
0
,
β
P
,
β
ϑ
and n parameters so that the quadratic
equation for the errors Q is reduced to a mini-
mum (see equation 11).
• If you like, you can adjust the vernier scale
around s
0
so that this correction is not necessary.
With the set parameters, it is possible to calculate the
“effective” piston displacement s from the measured
displacement s
e
using Equation 9 and then to calcu-
late the calibrated measuring cell volume using Equa-
tion 8.
Sample measurements:
Table 1: Measured values for calibration
i s
e
/ mm ϑ p / bar
1 40.0 20.0°C 6.6
2 20.0 20.0°C 12.4
3 10.0 20.0°C 23.3
4 5.0 20.0°C 41.8
5 3.5 20.0°C 53.9
6 5.0 20.0°C 41.8
7 5.0 10.0°C 38.9
8 5.0 30.0°C 45.3
9 5.0 40.0°C 49.0
10 5.0 50.0°C 53.5
The following parameter values are obtained:
s
0
= 0.19 mm,
bar
mm
023 0
P
.
= β
,
grd
mm
034 0.
= β
ϑ
and
n = 0.00288 mol.
7. Filling with test gas
7.1 Handling of sulphur hexafluoride:
Sulphur hexafluoride (SF
6
) is a non-toxic gas and is
absolutely safe for humans. The MAC value for danger
of suffocation on account of oxygen deprivation is
1000 ppm. That is equivalent to 6 filled measuring
cells per 1 m
3 of air.
However, SF
6
is extremely harmful to the environment
and can give rise to a greenhouse effect 24,000 times
stronger than CO
2
. Therefore, do not allow large quan-
tities to be released into the environment.
7.2 Gas connection via fixed pipes:
Additionally required:
1 SF
6
gas cylinder with manufacturer’s/supplier’s rec-
ommended gas fittings/valves, e.g. SH ILB gas cylinder
and Y11 L215DLB180 regulating valve from Airgas
(www.airgas.com).
1 Pipes with outer diameter of 1/8" and, if necessary,
adapters, e.g. from Swagelok (www.swagelok.com).
1 open-end spanner (13 mm), 1 open-end spanner
(11 mm)
According to the principles of “good laboratory prac-
tice”, it is recommended to utilise a gas supply via
fixed pipes, especially if the equipment is regularly in
operation.